Why does GLIE+MC Control Algorithm use a single episode of Monte Carlo evaluation?
I feel the general answer is that we want to be as efficient as possible in learning from experience. 

Policy improvement here always produces an equivalent or better policy, so delaying the improvement step to gather more episodes will only slow down learning.

I would note too that often a different kind of Monte Carlo learning is used. Instead the speed of the update is typically controlled with a new hyper parameter $\alpha$, instead of keeping track of the visit counts. The Q estimate is then updated something like:

$$
Q \leftarrow Q + \alpha \left (G - Q \right)
$$

The value of $\alpha$ then lets you tune how much evaluation vs improvement happens. This is called constant alpha Monte Carlo. Often this is used as a stepping stone to introduce TD methods, e.g., in 6.1 of the Sutton and Barto book.